ANS:D - 0.5

When the sides of a slab simply supported on edges and spanning in two directions are equal, it indicates a square slab. For a square slab, the maximum bending moment is multiplied by a certain factor compared to a rectangular slab. This factor depends on the aspect ratio of the slab. For a square slab, the factor is typically around 0.5.

1. Slab Geometry:
   • Square Slab: A square slab has equal sides, meaning its length and width are the same.
   • Rectangular Slab: A rectangular slab has unequal sides, with one side longer than the other.
2. Load Distribution:
   • Square Slab: In a simply supported square slab, the load is distributed more evenly across both directions. Due to its symmetric nature, the load tends to cause bending moments that are more evenly distributed throughout the slab's span.
   • Rectangular Slab: In a rectangular slab, the longer side tends to carry a greater portion of the load compared to the shorter side. This results in higher bending moments along the longer span and lower bending moments along the shorter span.
3. Moment Redistribution:
   • Square Slab: The symmetric nature of a square slab results in a more uniform distribution of bending moments. Any increase in bending moment in one direction tends to be compensated by a decrease in bending moment in the other direction.
   • Rectangular Slab: In a rectangular slab, any increase in bending moment along the longer span may not be fully compensated by a decrease in bending moment along the shorter span. This can lead to higher overall bending moments in the rectangular slab compared to a square slab.
4. Empirical Factors:
   • Observation and Research: Through empirical observation and research, engineers have found that for square slabs simply supported on edges and spanning in two directions, the maximum bending moment tends to be around half that of a rectangular slab with the same total load and support conditions.
5. Design Considerations:
   • Conservative Approach: Using a factor of 0.5 for the maximum bending moment in square slabs ensures a conservative design approach. It provides a safety margin to account for variations in loads, material properties, and construction tolerances.
6. Analysis and Standards:
   • Structural Analysis: Structural engineers analyze slabs using various methods, including finite element analysis and simplified analytical approaches, to determine the distribution of bending moments.
   • Design Standards: Design standards and codes provide guidelines and equations for calculating bending moments in slabs. These standards often incorporate factors based on empirical data and engineering judgment to ensure safe and economical designs.